How can I create a material that has different levels of transparency on the front and back face in Cycles?
For a face without thickness, you could just use the Backfacing output of a Geometry node to make a switch between values:

(If you don't want unrealistic 1-sided refraction, set the marked IOR field to 1.. you could also use the switch to control, say, Alpha,which may work better for you.. or any other property in the material)
These are simple planes: the faces differ only in their normals-to-camera: